Scaling properties in off equilibrium dynamical processes

Abstract

In the present paper, we analyze the consequences of scaling hypotheses on dynamic functions, as two times correlations $C(t,t')$. We show, under general conditions, that $C(t,t')$ must obey the following scaling behavior $C(t,t') = ϕ_1(t)^{f(β)}{\cal{S}}(β)$, where the scaling variable is $β=β(ϕ_1(t')/ϕ_1(t))$ and $ϕ_1(t')$, $ϕ_1(t)$ two undetermined functions. The presence of a non constant exponent $f(β)$ signals the appearance of multiscaling properties in the dynamics.